Constructing Families of Solutions to an Integrable Time-Dependent Shallow Water Wave Equation in (1+1)-Dimensions

Abstract

In this paper, an integrable shallow water wave equation with timedependent coefficients in (1+1)-dimensions is taken into account. Through employing the generalized three-wave methods, a series of (double) solitary wave solutions and periodic (solitary) wave solutions to the considered equation are presented with the aid of symbolic calculation. Furthermore, by specifying relevant functions and parameters, the localized structures of some resulting solutions are displayed via some figures. These results enrich the diversity of nonlinear waves in physics.